The Elements of Euclid: With Dissertations Intended to Assist and Encourage a Critical Examination of These Elements as the Most Effectual Means of Establishing a Juster Taste Upon Mathematical Subjects Than that which at Present PrevailsPrinted at the Clarendon Press, 1781 - 309 Seiten |
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Seite 9
... rectilineal angle : for the angle is not changed by making the lines longer or fhorter ; but only by opening or ... figures which he defines . Definitions may be confidered as of two kinds ; firft , fuch as ferve only to explain the ...
... rectilineal angle : for the angle is not changed by making the lines longer or fhorter ; but only by opening or ... figures which he defines . Definitions may be confidered as of two kinds ; firft , fuch as ferve only to explain the ...
Seite 14
... figures , which are not true , but upon the fuppofition that the lines are in the fame plane , as I fhall have occafion to obferve . And the plane rectilineal angle is the inclination of two straight lines to one another in or upon fuch ...
... figures , which are not true , but upon the fuppofition that the lines are in the fame plane , as I fhall have occafion to obferve . And the plane rectilineal angle is the inclination of two straight lines to one another in or upon fuch ...
Seite 18
... figure which has been described or at least compleated ; and the third commonly to fimilar figures . own . Now these ... rectilineal figure is the triangle ; the dif ferent parts of which the learner ought to be familiarly acquainted ...
... figure which has been described or at least compleated ; and the third commonly to fimilar figures . own . Now these ... rectilineal figure is the triangle ; the dif ferent parts of which the learner ought to be familiarly acquainted ...
Seite 68
... rectilineal figure into a parallelogram , whatever be the number of its fides ; and whatever be their position to one another . Now I hope it is evident that Euclid had some other plan in his demonstrations than to convince the ...
... rectilineal figure into a parallelogram , whatever be the number of its fides ; and whatever be their position to one another . Now I hope it is evident that Euclid had some other plan in his demonstrations than to convince the ...
Seite 69
... rectilineal figure ; or with the circle as being bounded by one fingle line ; the circle might probably have the preference upon a full examination as being a perfect figure , and for other reasons which it would be too tedious to ...
... rectilineal figure ; or with the circle as being bounded by one fingle line ; the circle might probably have the preference upon a full examination as being a perfect figure , and for other reasons which it would be too tedious to ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD alfo alſo angle ABC angle BAC angle contained angle equal apply itſelf bafe baſe BC is equal Book certainly circle ABC circumference common notion confequences conft conftruction cut in halves demonftrated deſcribed diſtance drawn equal angles equiangular equilateral equimultiples Euclid exceed faid fame manner fame multiple fame parallels fame ratio fame reaſon fecond fegment fhall fides fimilar fince firſt fome fquare ftraight line BC fuch fuppofe fuppofition given rectilineal given ſtraight line Gnomon greater hath himſelf impoffible infcribed joined lefs leſs let the ftraight magnitudes moſt muſt neceffary parallelogram PROP propofition proportionals purpoſe reader reaſon rectangle contained rectilineal figure remaining angle remaining fides right angles ſame ſay ſhall ſhould ſome ſquare ſtraight line AB ſubject ſuch ſuppoſe taken theſe thoſe tiple triangle ABC underſtand uſe Wherefore becauſe
Beliebte Passagen
Seite 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 47 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Seite 68 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Seite 45 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.
Seite 15 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Seite 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 88 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Seite 42 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Seite 109 - Draw two diameters AC, BD of the circle ABCD, at right angles to one another; and through the points A, B. C, D, draw (17.
Seite 8 - GB is equal to E, and CK to F ; therefore AB is the same multiple of E, that KH is of F: But AB...